1. Field of the Invention
The present invention relates to a wavelength division multiplexer/demultiplexer having a flat wavelength response, and more particularly, to a wavelength division multiplexer/demultiplexer that makes the distribution of an optical signal input to an Arrayed Waveguide Grating (AWG) in a sinc-function shape and can obtain a flat wavelength response.
This work was supported by the IT R&D program of MIC/IITA [2007-S-011-01, Development of Optical Switches for ROADM].
2. Discussion of Related Art
In Wavelength Division Multiplexing (WDM) communication, a transmitter multiplexes optical signals having several wavelengths and transfers the multiplexed optical signals through one optical fiber, and a receiver demultiplexes the multiplexed optical signals according to the wavelengths and separately uses the respective optical signals. An AWG is used for such multiplexing/demultiplexing.
FIG. 1 illustrates a conventional wavelength division multiplexer/demultiplexer using an AWG.
Referring to FIG. 1, in a conventional wavelength division multiplexer/demultiplexer 100 using an AWG 114, the AWG 114 consisting of a plurality of arrayed waveguides having a specific optical path difference is coupled between first and second slab waveguides 112 and 116.
When a multiplexed signal is input from an input waveguide 110 to the wavelength division multiplexer/demultiplexer 100, it is passed through the first slab waveguide 112, demultiplexed into respective channels by the AWG 114, and output to output waveguides 118 through the second slab waveguide 116. On the other hand, when a plurality of optical signals having different wavelengths are input from the output waveguides 118, they are passed through the second slab waveguide 116, multiplexed by the AWG 114, and output to the input waveguide 110 through the first slab waveguide 112.
Such operations of the wavelength division multiplexer/demultiplexer 100 may be described by a grating equation, which describes a distribution characteristic of incident light according to diffraction by regarding the AWG 114 as a diffraction grating. This will be described in further detail below.
First, a wavelength focused on the central axis of the second slab waveguide 116 in a rear part satisfies Equation 1 below.
                                          β            ·            Δ                    ⁢                                          ⁢          L                =                                                                              2                  ⁢                                                                          ⁢                  π                                                  λ                  o                                            ·                              n                eff                            ·              Δ                        ⁢                                                  ⁢            L                    =                                    ±              2                        ⁢                                                  ⁢            m            ⁢                                                  ⁢            π                                              [                  Equation          ⁢                                          ⁢          1                ]            
In Equation 1, β denotes a propagation constant, neff denotes a mode refractive index of the input waveguide 110, λ0 denotes a center wavelength, m denotes a grating order of the AWG 114, and ΔL denotes a path difference of the AWG 114.
Here, a specific wavelength λ which has deviated from the center wavelength λ0 by λ1 (λ=λ0+λ1) crosses the central axis at a specific angle, and satisfies Equation 2 below.
                                                                        2                ⁢                                                                  ⁢                π                            λ                        ·                          n              eff                        ·            Δ                    ⁢                                          ⁢          L                =                                                            2                ⁢                                                                  ⁢                π                            λ                        ·                          n              slab                        ·            a            ·            θ                    ±                      2            ⁢                                                  ⁢            m            ⁢                                                  ⁢            π                                              [                  Equation          ⁢                                          ⁢          2                ]            
In Equation 2, λ denotes the specific wavelength which has deviated from the center wavelength λ0 by λ1, nslab denotes a mode refractive index of a slab waveguide, a denotes an interval between centers of the AWG 114, and θ denotes an angle with respect to the central axis.
Therefore, by simultaneously solving Equation 1 and Equation 2, the angle θ of the specific wavelength λ with respect to the central axis can be expressed as shown in Equation 3 below.
                                                        2              ⁢                                                          ⁢              π                        λ                    ·                      n            slab                    ·          a          ·          θ                =                  2          ⁢                                          ⁢                      π            ·            Δ                    ⁢                                          ⁢                      L            ⁡                          (                                                                    n                    eff                    λ                                    λ                                -                                                      n                    eff                                          λ                      0                                                                            λ                    o                                                              )                                                          [                  Equation          ⁢                                          ⁢          3                ]                                θ        =                                            Δ              ⁢                                                          ⁢              L                        a                    ⁢                      (                                                            n                  eff                  λ                                                  n                  slab                  λ                                            -                                                                    n                    eff                                          λ                      o                                                                            n                    slab                                          λ                      o                                                                      ·                                  λ                                      λ                    o                                                                        )                                                          
In Equation 3, λ0 denotes the center wavelength, λ denotes the specific wavelength which has deviated from the center wavelength λ0 by λ1, neff denotes the mode refractive index of the input waveguide 110, nslab denotes the mode refractive index of the slab waveguide, a denotes an interval between centers of the AWG 114, θ denotes the angle with respect to the central axis, and ΔL denotes the path difference of the AWG 114.
Meanwhile, the power of light output to the output waveguides 118 while crossing the central axis at the angle θ can be expressed as shown in Equation 4 below.
                              E          θ                =                              ∑                          j              =              1                        n                    ⁢                                          ⁢                                    f              j                        ·                          g              j                        ·                          exp              ⁡                              (                                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                                      ⅈ                    ·                                                                  n                        eff                        λ                                            λ                                        ·                    j                                    ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                  L                                )                                                                        [                  Equation          ⁢                                          ⁢          4                ]            
In Equation 4, fj denotes an optical coupling coefficient of an optical signal transferred from the input waveguide 110 to the AWG 114, gj denotes an optical coupling coefficient of an optical signal transferred from the AWG 114 to the output waveguides 118, the exponential function denotes a change in phase caused by a path difference between respective arrayed waveguides, and n denotes a total number of arrayed waveguides of the AWG 114.
In the case of the optical coupling coefficient fj, all inputs are transferred along the central axis of the input waveguide 110 and thus have the same phase. On the other hand, in the case of the optical coupling coefficient gj, inputs cross the central axis at the angle θ. Thus, in consideration of a change in phase according to the angle θ with respect to the central axis, the optical coupling coefficient gj can be expressed as shown in Equation 5 below.
                              g          j                =                              f            j                    ·                      exp            ⁡                          (                              2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                                  ⅈ                  ·                                                            n                      slab                      λ                                        λ                                    ·                  j                                ⁢                                                                  ⁢                a                ⁢                                                                  ⁢                θ                            )                                                          [                  Equation          ⁢                                          ⁢          5                ]            
By inserting the optical coupling coefficient gj obtained through Equation 5 into Equation 4, the power of an output optical signal can be expressed as shown in Equation 6 below.
                              E          θ                =                              ∑                          j              =              1                        n                    ⁢                                          ⁢                                                    f                j                2                            ·              exp                        ⁢                          {                              2                ⁢                                                                  ⁢                                  πⅈ                  ·                                      j                    ⁡                                          (                                                                                                                                                                  n                                eff                                λ                                                            λ                                                        ·                            Δ                                                    ⁢                                                                                                          ⁢                          L                                                +                                                                                                                                            n                                slab                                λ                                                            λ                                                        ·                            a                                                    ⁢                                                                                                          ⁢                          θ                                                                    )                                                                                  }                                                          [                  Equation          ⁢                                          ⁢          6                ]            
In Equation 6, the optical coupling coefficient fj denotes the power of each optical signal output through the output waveguides 118 and thus can be calculated by an overlap integral between a slab mode and a waveguide mode, a Beam-Propagation Method (BPM), or so on.
Therefore, when the input waveguide 110 crosses the central axis at an angle θin, and the output waveguides 118 cross the central axis at an angle θout, the optical coupling coefficients and the power of an optical signal output to the output waveguides 118 can be expressed as shown in Equation 7 below.
                                          f            j                    =                                    f              jo                        ·                          exp              (                              2                ⁢                                                                  ⁢                                  πⅈ                  ·                                                            n                      slab                      λ                                        λ                                    ·                  ja                                ⁢                                                                  ⁢                                  θ                  in                                            )                                      ⁢                                  ⁢                              g            j                    =                                    f              jo                        ·                          exp              (                              2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                                  ⅈ                  ·                                                            n                      slab                      λ                                        λ                                    ·                  ja                                ⁢                                                                  ⁢                                  θ                  out                                            )                                      ⁢                                  ⁢                  E          ⁡                      (                                          θ                in                            ,                              θ                out                                      )                          =                              ∑                          j              =              1                        n                    ⁢                                    f              j              2                        ⁢            exp            ⁢                          {                              2                ⁢                                                                  ⁢                                  πⅈ                  ·                                      j                    λ                                                  ⁢                                  (                                                                                                              n                          eff                          λ                                                ·                        Δ                                            ⁢                                                                                          ⁢                      L                                        +                                                                  n                        slab                        λ                                            ·                                              a                        ⁡                                                  (                                                                                    θ                              in                                                        +                                                          θ                              out                                                                                )                                                                                                      )                                            }                                                          [                  Equation          ⁢                                          ⁢          7                ]            
Referring to Equation 7, there is a Fourier-transform relationship between an optical signal input to the first and second slab waveguides 112 and 116 at the specific angle θin and an optical signal output from the first and second slab waveguides 112 and 116 at the specific angle θout.
Therefore, to obtain a flat wavelength response, an optical signal input to the AWG 114 must have a sinc-function distribution.
However, the distribution of an input optical signal input to the input waveguide 110 is generally similar to a Gaussian distribution. Thus, an output signal output from the output waveguides 118 is also expected to have the Gaussian distribution.
A wavelength division multiplexer/demultiplexer having a Gaussian wavelength response narrows the available wavelength range of a light source in a communication system. Therefore, the light source is required to have high wavelength stability, and the establishment and maintenance cost of the communication system increases.
Consequently, to implement a wavelength division multiplexer/demultiplexer having a flat wavelength response, the distribution of an optical signal input to the AWG 114 must be made in the sinc-function shape, as mentioned above. To this end, the following methods have been disclosed.
According to a first method, the phase and loss of an AWG are adjusted such that the optical signal distribution of the AWG becomes similar to the sinc-function shape.
However, with respect to the length of the AWG, the length of the AWG in a specific section corresponding to a negative value of the sinc function must be adjusted to have a difference of a half wavelength, and an additional loss must be artificially caused in an optical waveguide. Thus, the first method is difficult to implement and also increases the insertion loss of a wavelength division multiplexer/demultiplexer by the amount of the additional loss of the AWG.
According to a second method, a parabolic horn waveguide is interposed in a boundary between an input waveguide and a first slab waveguide to make a double-peak-shape light distribution, and then the light distribution is projected to the output of a second slab waveguide as is, such that a combined optical signal has double peaks with respect to a wavelength in an output waveguide.
However, the second method requires a horn waveguide having a very complicated structure, and the horn waveguide must have a considerably large size to make a double-peak light distribution at the boundary between the input waveguide and the first slab waveguide. Thus, the overall size of a wavelength division multiplexer/demultiplexer considerably increases.
According to a third method, a multimode taper is interposed in a boundary between a second slab waveguide and an output waveguide to obtain a flat wavelength response using a coupling between the output waveguide and a high-order mode of a taper end.
However, when the width of the taper is small, the wavelength response becomes similar to the Gaussian distribution. To obtain a flat wavelength response characteristic, the width of the taper must be large to have a sufficient number of modes at the taper end. For this reason, the width of the output waveguide also increases, and the overall size of a wavelength division multiplexer/demultiplexer increases. In addition, several modes are blocked while being transferred from the taper to the single mode waveguide, and thus total insertion loss increases.